Nonexistence Of Parameters - 1

There are networks in which z and y parameters do not both exist. For example, consider a 2-port network consisting of a single series element as shown in Fig. a. The y-parameter matrix for this network is

(a)

(b)

FIG. Single-dement networks (a) Single series element

(b) Single shunt dement

?y =

Since ?y is zero, the z parameters as determined from they parameters do not exist.

As another example of a network which does not have both z and y parameters, consider a 2-port consisting of a single shunt element as shown in Fig. b. The z parameters matrix for this network is

Δz = Z × Z – Z × Z = 0

Since the determinant ?z is zero, the y parameters as determined from the z parameters do not exist.

For some networks, neither the z nor the y parameters exist. As an example of this, consider the ideal transformer shown in Fig.

The defining equations are

V1 = nV2

I1 = –1/n I2

Since these equations require that the voltage at one port be specified as a function of

FIG. Ideal transformer

voltage at the other port, and similarly that the current at one port be expressed in terms of the current at the other port, neither the z parameters nor the y parameters exist for an ideal transformer.

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